Chapter 4 Forces and the Laws of Motion WHAT IS A FORCE? An object’s interaction with its environment. Example: Hitting a baseball with a bat would cause the two to interact. They would then exert a force on each other.
These interactions are through
Contact forces that touch, like the ball and bat
Field forces that do not touch; they act over a distance
Gravitational fields act on objects. If your lab partner was walking along and missed a step, they would fall to the ground. A giant hand would not come from the earth and pull them down, but the Earth would indirectly exert enough force to make your partner hit the ground.
Magnetic fields are what cause magnets to stick together. When you hold two magnets in your hand and slowly bring them together, you can feel either an attraction or repulsion between the two. The magnets never touch, but if you let them go, their force would either make them touch or repel each other.
Other field forces include electricity, but this chapter is most concerned with gravity.
Because a force involves interaction between objects, it will cause a change in the object’s motion. The object's velocity will either increase or decrease. When you push a chair, you apply a force to increase it's velocity and move it across the room. In order to stop an apple from falling, you apply a force to decrease its velocity and end its motion.
HOW IS IT MEASURED? Force may be measured in three systems. For our purposes, we use the SI system.
System
Mass
Acceleration
Force
Derivation
SI (Système Internationale)
kg
m/s2
N
kg* m/s2
CGS (Centimeter, Gram, Second)
g
cm/s2
dyne
g* cm/s2
Avoirdupois (Customary System)
slug
ft/s2
lb
slug*ft/s2
HOW DO WE FIND FORCE? Force Diagramsare useful to show the forces acting on an object. Forces are vectors, meaning they have both a magnitude (size) and direction. Free-body diagrams isolate and show the forces acting on an object, which helps you analyze the situation. free-body diagram (Professor Andy Gavrin, Indiana University Purdue University at Indianapolis)
After we lay out the forces acting on an object, we can analyze them using Newton's Laws of Motion. FIRST LAW (Section 4-2) "An object at rest remains at rest, and an object in motion continues in motion with constant velocity unless the object experiences a net external force" (Book) Basically, an object will keep moving the way it is moving unless a force is applied to accelerate it. This tendency to keep motion the same is called inertia. *An object can still move if no net force acts on it*
Mass is a measurement of inertia. The more mass an object has the harder it is to move. It takes far more effort to throw a bowling ball across the room than a piece of chalk. Mass is what resists this acceleration.
When an object moves with a constant velocity, the forces acting on it are equal to zero. This state is called equilibrium.
If the object is at rest, and the sum of the forces acting on the object is still zero, then it is in static equilibrium.
To determine the net external force (εF) on an object we use free-body diagrams.
Problems (Pg 132-133) 2. A crate is pulled to the right with a force of 82.0N, to the left with a force of 115N, upward with a force of 565N, and downward with a force of 236N.
A. Find the net external force in the x direction
B. Find the net external force in the y direction
C. Find the magnitude and direction of the net external force on the crate
2a. Using the frame of reference that left is negative and right is positive: εFx = 82.0N – 115N
= -33N
2b. Frame of reference: Up is positive and down is negative: εFy = 565N - 236N
= 329 N
2c. Pythagorean Theorem a2 + b2 = c2
Draw a triangle with sides A and B as -33N and 329N
Use the formula and solve with algebra
c2 = (-33N)2 + (329N)2
c2 = 109330N
c = 331N
To find the angle, use inverse tangent
θ = tan-1(329/33)
θ = 84.3 degrees North by West
Make sure after you list the angle you write the order in which you put the directions in the inverse tangent function.
SECOND LAW(Section 4-3) "The acceleration of an object is directly proportional to the net external force acting on the object and inversely proportional to the object's mass" (Book) εF = ma The force acting on an object is equal to its mass multiplied by its acceleration. We can now use the second law to remember the first law because when the sum of the forces is equal to zero, the acceleration is zero.
Problems (pg 138) 1. The net external force on the propeller of a 3.2 kg model airplane is 7.0N forward. What is the acceleration of the airplane?
F = ma
7.0N = (3.2kg)a
2.2m/s^2 forward = a
5. A soccer ball kicked with a force of 13.5N accelerates at 6.5m/s^2 to the right. What is the mass of the ball?
F = ma
13.5N = m(6.5m/s^2)
2.1kg = m
THIRD LAW(Section 4-3) "If two objects interact, the magnitude of the force exerted on object 1 by object 2 is equal to the magnitude of the force simultaneously exerted on object 2 by object 1, and these two forces are opposite in direction" (Book)
When two object interact they will have equal, but opposite forces. These forces are called action-reaction pairs. These two forces occur at exactly the same time. Though they are pairs, the forces do not act on the same object. When you dial a phone number, your fingers exert a force on the keys and the keys exert a force on your fingers. The keys cannot exert a force on themselves, so when we analyze the forces at them, we omit the reaction force on your fingers.
Contact forces are not the only forces that have action reaction pairs. Field forces also have action reaction pairs. When a bowling ball falls the Earth exerts a force on it. The ball also exerts a force on the Earth. Why don't we notice it? If you remember the formula for force, it is equal to mass multiplied by acceleration. The Earth is so large that its acceleration is tiny. On the other hand, the bowling ball does not have as much mass and accelerates a large amount. Problems (140) 1. A 6.0kg object undergoes an acceleration of 2.0m/s^2.
A. What is the magnitude of the net external force acting on it?
B. If this same force is applied to a 4.0kg object, what acceleration is produced? 1a. F = ma F = (6.0kg)(2.0m/s^2) F = 12.0 N 1b. F = ma 12.0N = (4.0kg)a 3.0m/s^2 = a 2. A child pulls a wagon with a horizontal force, causing it to accelerate. Newton’s third law says that the wagon exerts an equal and opposite force on the child. How can the wagon accelerate? (Hint: draw a free-body diagram for each object to help you answer this question). The wagon exerts a force on the child’s hand, not itself. A free-body diagram of the wagon would show gravity, the force of friction, and the force of the child acting on the wagon.
EVERYDAY FORCES (Section 4-4) Weight is the force of gravity on an object. To find it multiply the mass of the object (in kilograms) by 9.81m/s^2.
The normal force is the force that holds an object up and makes sure your dresser doesn't fall through the floor. Normal Force is perpendicular with the surface at the point of contact. Many times, normal force and gravity combine to create equilibrium. Normal force is always ninety degrees from where it contacts an object, and may not always be opposite in direction to the force of gravity. Normal force = mgcosθ FRICTION As an object starts to move, a force known as static friction opposes motion as long as the force is greater than the force being applied in the same direction the object is moving.
The coefficient of static friction is found by dividing the maximum force of static friction divided by the normal force
To calculate the maximum force of static friction= Normal force * Coefficient of static friction NOTE: The direction of the force of static friction is opposite than that of the direction of motion.
When an object is sliding against a surface, a force known as kinetic friction opposes the motion of the object.
The coefficient of kinetic friction is found by dividing the maximum force of kinetic friction divided by the normal force.
To calculate the maximum force of kinetic friction= Normal force * Coefficient of kinetic friction NOTE: The direction fo the force of kinetic friction is opposite than that of the direction of motion.
Force of friction between two objects depends on the coefficient of friction and the normal force
-For objects at rest, frictional force is dependent upon the amount of force applied.
The force of gravity exerted by the earth is a vector quanitity directed toward the center of the earth. The magnitude of this force is a scalar quantity known as weight.
All information used in this wiki came from Holt Physics Textbook and Classnotes. The link to the freebody diagram came from Gavrin, Andy. “Newton’s Laws of Motion 1.” Web Physics. 8 Jan. 2009
<webphysics.iupui.edu/152/152Basics/newton/gif/newtpic07.gif>.
WHAT IS A FORCE?
An object’s interaction with its environment. Example: Hitting a baseball with a bat would cause the two to interact. They would then exert a force on each other.
These interactions are through
Because a force involves interaction between objects, it will cause a change in the object’s motion. The object's velocity will either increase or decrease. When you push a chair, you apply a force to increase it's velocity and move it across the room. In order to stop an apple from falling, you apply a force to decrease its velocity and end its motion.
HOW IS IT MEASURED?
Force may be measured in three systems. For our purposes, we use the SI system.
HOW DO WE FIND FORCE?
Force Diagrams are useful to show the forces acting on an object. Forces are vectors, meaning they have both a magnitude (size) and direction. Free-body diagrams isolate and show the forces acting on an object, which helps you analyze the situation.
free-body diagram (Professor Andy Gavrin, Indiana University Purdue University at Indianapolis)
After we lay out the forces acting on an object, we can analyze them using Newton's Laws of Motion.
FIRST LAW (Section 4-2)
"An object at rest remains at rest, and an object in motion continues in motion with constant velocity unless the object experiences a net external force" (Book) Basically, an object will keep moving the way it is moving unless a force is applied to accelerate it. This tendency to keep motion the same is called inertia. *An object can still move if no net force acts on it*
Mass is a measurement of inertia. The more mass an object has the harder it is to move. It takes far more effort to throw a bowling ball across the room than a piece of chalk. Mass is what resists this acceleration.
When an object moves with a constant velocity, the forces acting on it are equal to zero. This state is called equilibrium.
If the object is at rest, and the sum of the forces acting on the object is still zero, then it is in static equilibrium.
To determine the net external force (εF) on an object we use free-body diagrams.
Problems (Pg 132-133)
2. A crate is pulled to the right with a force of 82.0N, to the left with a force of 115N, upward with a force of 565N, and downward with a force of 236N.
A. Find the net external force in the x direction
B. Find the net external force in the y direction
C. Find the magnitude and direction of the net external force on the crate
2a. Using the frame of reference that left is negative and right is positive:
εFx = 82.0N – 115N
= -33N
2b. Frame of reference: Up is positive and down is negative:
εFy = 565N - 236N
= 329 N
2c. Pythagorean Theorem a2 + b2 = c2
Draw a triangle with sides A and B as -33N and 329N
Use the formula and solve with algebra
c2 = (-33N)2 + (329N)2
c2 = 109330N
c = 331N
To find the angle, use inverse tangent
θ = tan-1(329/33)
θ = 84.3 degrees North by West
Make sure after you list the angle you write the order in which you put the directions in the inverse tangent function.
SECOND LAW (Section 4-3)
"The acceleration of an object is directly proportional to the net external force acting on the object and inversely proportional to the object's mass" (Book)
εF = ma
The force acting on an object is equal to its mass multiplied by its acceleration. We can now use the second law to remember the first law because when the sum of the forces is equal to zero, the acceleration is zero.
Problems (pg 138)
1. The net external force on the propeller of a 3.2 kg model airplane is 7.0N forward. What is the acceleration of the airplane?
F = ma
7.0N = (3.2kg)a
2.2m/s^2 forward = a
5. A soccer ball kicked with a force of 13.5N accelerates at 6.5m/s^2 to the right. What is the mass of the ball?
F = ma
13.5N = m(6.5m/s^2)
2.1kg = m
THIRD LAW (Section 4-3)
"If two objects interact, the magnitude of the force exerted on object 1 by object 2 is equal to the magnitude of the force simultaneously exerted on object 2 by object 1, and these two forces are opposite in direction" (Book)
When two object interact they will have equal, but opposite forces. These forces are called action-reaction pairs. These two forces occur at exactly the same time. Though they are pairs, the forces do not act on the same object. When you dial a phone number, your fingers exert a force on the keys and the keys exert a force on your fingers. The keys cannot exert a force on themselves, so when we analyze the forces at them, we omit the reaction force on your fingers.
Contact forces are not the only forces that have action reaction pairs. Field forces also have action reaction pairs. When a bowling ball falls the Earth exerts a force on it. The ball also exerts a force on the Earth. Why don't we notice it? If you remember the formula for force, it is equal to mass multiplied by acceleration. The Earth is so large that its acceleration is tiny. On the other hand, the bowling ball does not have as much mass and accelerates a large amount.
Problems (140)
1. A 6.0kg object undergoes an acceleration of 2.0m/s^2.
A. What is the magnitude of the net external force acting on it?
B. If this same force is applied to a 4.0kg object, what acceleration is produced?
1a. F = ma
F = (6.0kg)(2.0m/s^2)
F = 12.0 N
1b. F = ma
12.0N = (4.0kg)a
3.0m/s^2 = a
2. A child pulls a wagon with a horizontal force, causing it to accelerate. Newton’s third law says that the wagon exerts an equal and opposite force on the child. How can the wagon accelerate? (Hint: draw a free-body diagram for each object to help you answer this question).
The wagon exerts a force on the child’s hand, not itself. A free-body diagram of the wagon would show gravity, the force of friction, and the force of the child acting on the wagon.
EVERYDAY FORCES (Section 4-4)
Weight is the force of gravity on an object. To find it multiply the mass of the object (in kilograms) by 9.81m/s^2.
The normal force is the force that holds an object up and makes sure your dresser doesn't fall through the floor. Normal Force is perpendicular with the surface at the point of contact. Many times, normal force and gravity combine to create equilibrium. Normal force is always ninety degrees from where it contacts an object, and may not always be opposite in direction to the force of gravity. Normal force = mgcosθ
FRICTION
As an object starts to move, a force known as static friction opposes motion as long as the force is greater than the force being applied in the same direction the object is moving.
The coefficient of static friction is found by dividing the maximum force of static friction divided by the normal force
To calculate the maximum force of static friction= Normal force * Coefficient of static friction
NOTE: The direction of the force of static friction is opposite than that of the direction of motion.
When an object is sliding against a surface, a force known as kinetic friction opposes the motion of the object.
The coefficient of kinetic friction is found by dividing the maximum force of kinetic friction divided by the normal force.
To calculate the maximum force of kinetic friction= Normal force * Coefficient of kinetic friction
NOTE: The direction fo the force of kinetic friction is opposite than that of the direction of motion.
Force of friction between two objects depends on the coefficient of friction and the normal force
-For objects at rest, frictional force is dependent upon the amount of force applied.
The force of gravity exerted by the earth is a vector quanitity directed toward the center of the earth. The magnitude of this force is a scalar quantity known as weight.
You will find it extremely helpful to use the review page given at the end of the chapter. If you cannot find it...http://www.tomstrong.org/physics/fall08h.pdf
All information used in this wiki came from Holt Physics Textbook and Classnotes. The link to the freebody diagram came from
Gavrin, Andy. “Newton’s Laws of Motion 1.” Web Physics. 8 Jan. 2009
<webphysics.iupui.edu/152/152Basics/newton/gif/newtpic07.gif>.
The link to the review sheets was from Mr. Strong's website http://www.tomstrong.org/physics/fall08h.pdf